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Simplex Lock Project Description Prerequisites Warm up Problems Hints Resources Teaching Notes Extension Problems Results
Subsets in Sequence: An Investigation into Changing Places

The set {a, b, c} has exactly eight subsets.

  1. List all the subsets of {a, b, c}.
  2. Now arrange those subsets in a sequence so that each subset in the sequence differs from the one before it in one of two ways:
    • One new element is inserted:
      Example 1: {a}, {a, b}
      Example 2: {a, b}, {a, b, c}
    • One old element removed
      Example 1: {a, b, c}, {a, c}
      Example 2: {b},
  3. Can you create more than one sequence that fits these criteria?
  4. Create a listing like this for the subsets of {a, b, c, d}.
  5. Describe a general method (or explain why there isn’t one) for creating such a sequence of the subsets of any set {a1, a2, a3, ...an}.

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